(x-y)(x^2+xy+y^2) Formula

3 min read Jun 17, 2024
(x-y)(x^2+xy+y^2) Formula

Understanding the (x-y)(x^2 + xy + y^2) Formula

The formula (x-y)(x^2 + xy + y^2) is a special case of a more general algebraic concept known as the difference of cubes. It provides a quick and efficient way to factor expressions that fit a specific pattern.

The Difference of Cubes Formula

The general formula for the difference of cubes is:

a³ - b³ = (a - b)(a² + ab + b²)

This formula states that the difference of two cubes can be factored into the product of the difference of their cube roots and a quadratic expression.

Applying the Formula to (x-y)(x^2 + xy + y^2)

In our specific case, we can see that:

  • a = x
  • b = y

Therefore, applying the difference of cubes formula, we get:

(x³ - y³) = (x - y)(x² + xy + y²)

How to Use the Formula

The formula is useful for:

  • Factoring expressions: If you encounter an expression in the form a³ - b³, you can immediately factor it using the formula.
  • Simplifying expressions: By factoring, you can often simplify complex expressions, making them easier to work with.
  • Solving equations: The formula can be used to solve equations involving the difference of cubes.


Factor the expression x³ - 8

  1. Recognize that 8 is the cube of 2 (2³ = 8).
  2. Apply the difference of cubes formula:
    • a = x
    • b = 2
  3. (x³ - 2³) = (x - 2)(x² + 2x + 4)

Therefore, the factored form of x³ - 8 is (x - 2)(x² + 2x + 4).


The (x-y)(x² + xy + y²) formula, derived from the difference of cubes formula, provides a valuable tool for factoring and simplifying expressions. Understanding this formula can save you time and effort when working with algebraic expressions.

Related Post

Featured Posts